Compared with conventional methods of fault diagnosis for power transformers, which have defects such as imperfect encoding and too absolute encoding boundaries, this paper systematically discusses various intelligent approaches applied in fault diagnosis and decision making for large oil-immersed power transformers based on dissolved gas analysis (DGA), including expert system (EPS), artificial neural network (ANN), fuzzy theory, rough sets theory (RST), grey system theory (GST), swarm intelligence (SI) algorithms, data mining technology, machine learning (ML), and other intelligent diagnosis tools, and summarizes existing problems and solutions. From this survey, it is found that a single intelligent approach for fault diagnosis can only reflect operation status of the transformer in one particular aspect, causing various degrees of shortcomings that cannot be resolved effectively. Combined with the current research status in this field, the problems that must be addressed in DGA-based transformer fault diagnosis are identified, and the prospects for future development trends and research directions are outlined. This contribution presents a detailed and systematic survey on various intelligent approaches to faults diagnosing and decisions making of the power transformer, in which their merits and demerits are thoroughly investigated, as well as their improvement schemes and future development trends are proposed. Moreover, this paper concludes that a variety of intelligent algorithms should be combined for mutual complementation to form a hybrid fault diagnosis network, such that avoiding these algorithms falling into a local optimum. Moreover, it is necessary to improve the detection instruments so as to acquire reasonable characteristic gas data samples. The research summary, empirical generalization and analysis of predicament in this paper provide some thoughts and suggestions for the research of complex power grid in the new environment, as well as references and guidance for researchers to choose optimal approach to achieve DGA-based fault diagnosis and decision of the large oil-immersed power transformers in preventive electrical tests.